The document discusses ideal operational amplifiers and their characteristics. It describes how an operational amplifier is a differential amplifier that takes the difference between signals at its two inputs and amplifies that difference. An ideal op-amp has infinite voltage gain, infinite input impedance, zero output impedance, infinite bandwidth, and zero offset voltage. However, real op-amps have limitations compared to these ideal characteristics. The document provides examples of calculating gain and bandwidth using typical op-amp specifications. It also briefly mentions some common op-amp applications and types.

1. Operational Amplifiers Navigation
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Ideal Operational Amplifier
As well as resistors and capacitors, Operational Amplifiers, or Op-amps as they are
more commonly called, are one of the basic building blocks of Analogue Electronic
Circuits. It is a linear device that has all the properties required for nearly ideal DC
amplification and is used extensively in signal conditioning, filtering or to perform
mathematical operations such as add, subtract, integration and differentiation. An ideal
Operational Amplifier is basically a 3-terminal device that consists of two high
impedance inputs, one an Inverting input marked with a negative sign, ("-") and the
other a Non-inverting input marked with a positive plus sign ("+").
The amplified output signal of an Operational Amplifier is the difference between the
two signals being applied to the two inputs. In other words the output signal is a
differential signal between the two inputs and the input stage of an Operational Amplifier
is in fact a differential amplifier as shown below.
Differential Amplifier
The circuit shows a generalized form
of a differential amplifier with two
inputs marked V1 and V2. The two
identical transistors TR1 and TR2 are
both biased at the same operating
point with their emitters connected
together and returned to the common
rail, -Vee by way of resistor Re. The
circuit operates from a dual supply
+Vcc and -Vee which ensures a
constant supply. The voltage that
appears at the output, Vout of the
amplifier is the difference between
the two input signals as the two base
inputs are in anti-phase with each
other. So as the forward bias of
transistor, TR1 is increased, the
forward bias of transistor TR2 is
reduced and vice versa. Then if the
two transistors are perfectly matched,
the current flowing through the

2. common emitter resistor, Re will
remain constant.
Like the input signal, the output signal is also balanced and since the collector voltages
either swing in opposite directions (anti-phase) or in the same direction (in-phase) the
output voltage signal, taken from between the two collectors is, assuming a perfectly
balanced circuit the zero difference between the two collector voltages. This is known as
the Common Mode of Operation with the common mode gain of the amplifier being the
output gain when the input is zero.
Ideal Operational Amplifiers also have one output (although there are ones with an
additional differential output) of low impedance that is referenced to a common ground
terminal and it should ignore any common mode signals that is, if an identical signal is
applied to both the inverting and non-inverting inputs there should no change to the
output. However, in real amplifiers there is always some variation and the ratio of the
change to the output voltage with regards to the change in the common mode input
voltage is called the Common Mode Rejection Ratio or CMRR.
Operational Amplifiers on their own have a very high open loop DC gain and by
applying some form of Negative Feedback we can produce an operational amplifier
circuit that has a very precise gain characteristic that is dependant only on the feedback
used. An operational amplifier only responds to the difference between the voltages on its
two input terminals, known commonly as the "Differential Input Voltage" and not to their
common potential. Then if the same voltage potential is applied to both terminals the
resultant output will be zero. An Operational Amplifiers gain is commonly known as the
Open Loop Differential Gain, and is given the symbol (Ao).
Equivalent Circuit for Ideal Operational Amplifiers
Idealized Characteristics.

3. PARAMETER IDEALIZED CHARACTERISTIC
Voltage Gain, (A) Infinite - The main function of an operational amplifier
is to amplify the input signal and the more open loop
gain it has the better, so for an ideal amplifier the gain
will be infinite.
Input impedance, (Zin) Infinite - Input impedance is assumed to be infinite to
prevent any current flowing from the source supply into
the amplifiers input circuitry.
Output impedance, (Zout) Zero - The output impedance of the ideal operational
amplifier is assumed to be zero so that it can supply as
much current as necessary to the load.
Bandwidth, (BW) Infinite - An ideal operational amplifier has an infinite
Frequency Response and can amplify any frequency
signal so it is assumed to have an infinite bandwidth.
Offset Voltage, (Vio) Zero - The amplifiers output will be zero when the
voltage difference between the inverting and non-
inverting inputs is zero.
From these "idealized" characteristics above, we can see that the input resistance is
infinite, so no current flows into either input terminal (the current rule) and that the
differential input offset voltage is zero (the voltage rule). It is important to remember
these two properties as they help understand the workings of the amplifier with regards to
analysis and design of operational amplifier circuits.
However, real Operational Amplifiers such as the commonly available uA741, for
example do not have infinite gain or bandwidth but have a typical "Open Loop Gain"
which is defined as the amplifiers output amplification without any external feedback
signals connected to it and for a typical operational amplifier is about 100dB at DC (zero
Hz). This output gain decreases linearly with frequency down to "Unity Gain" or 1, at
about 1MHz and this is shown in the following open loop gain response curve.
Open-loop Frequency Response Curve

4. From this frequency response curve we can see that the product of the gain against
frequency is constant at any point along the curve. Also that the unity gain (0dB)
frequency also determines the gain of the amplifier at any point along the curve. This
constant is generally known as the Gain Bandwidth Product or GBP.
Therefore, GBP = Gain x Bandwidth or A x BW.
For example, from the graph above the gain of the amplifier at 100kHz = 20dB or 10,
then the
GBP = 100,000Hz x 10 = 1,000,000.
Similarly, a gain at 1kHz = 60dB or 1000, therefore the
GBP = 1,000 x 1,000 = 1,000,000. The same!.
The Voltage Gain (A) of the amplifier can be found using the following formula:
and in Decibels or (dB) is given as:

5. An Operational Amplifiers Bandwidth
The operational amplifiers bandwidth is the frequency range over which the voltage gain
of the amplifier is above 70.7% or -3dB (where 0dB is the maximum) of its maximum
output value as shown below.
Here we have used the 40dB line as an example. The -3dB or 70.7% of Vmax down point
from the frequency response curve is given as 37dB. Taking a line across until it
intersects with the main GBP curve gives us a frequency point just above the 10kHz line
at about 12 to 15kHz. We can now calculate this more accurately as we already know the
GBP of the amplifier, in this particular case 1MHz.
Example No1.
Using the formula 20 log (A), we can calculate the bandwidth of the amplifier as:
37 = 20 log A therefore, A = anti-log (37 ÷ 20) = 70.8
GBP ÷ A = Bandwidth, therefore, 1,000,000 ÷ 70.8 = 14,124Hz, or 14kHz
Then the bandwidth of the amplifier at a gain of 40dB is given as 14kHz as previously
predicted from the graph.
Example No2.
If the operational amplifiers gain was reduced by half to say 20dB in the above frequency
response curve, the -3dB point would now be at 17dB. This would then give us an overall

6. gain of 7.08, therefore A = 7.08. If we use the same formula as above this new gain
would give us a bandwidth of 141.2kHz, ten times more than at 40dB. It can therefore be
seen that by reducing the overall open loop gain of an operational amplifier its bandwidth
is increased and visa versa. The -3dB point is also known as the "half power point", as
the output power of the amplifier is at half its maximum value at this point.
Op-amp types
Operational amplifiers can be connected using external resistors or capacitors in a
number of different ways to form basic "building Block" circuits such as, Inverting, Non-
Inverting, Voltage Follower, Summing, Differential, Integrator and Differentiator type
amplifiers. There are a very large number of operational amplifier IC's available to suit
every possible application such as bipolar standard, precision, high-speed, low-noise,
high-voltage, etc and again with internal JFET transistors.
The most commonly available and used of all operational amplifiers is the industry
standard μA-741.